1. Field of the Invention
The present invention relates generally to a tunable active inductor, and in particular, to an active inductor with a high quality factor (Q factor) and a wide operating range, available for various radio frequency (RF) devices.
2. Description of the Related Art
With the recent increasing demand for wireless personal communication systems, low-price and integrated processing technologies are required to reduce production cost and system size.
The most preferable technology for wireless communication systems operating at 5 GHz or below to meet this requirement is the Complementary Metal-Oxide Semiconductor (CMOS) technology. However, when standard COMS technology is used for an RF part, the CMOS suffers a loss of microwave signals from silicon substrates with low resistance. It has proven to be extremely difficult to implement a high-quality spiral inductor with silicon substrates having great microwave signal loss.
Recently, therefore, several research groups have implemented the spiral inductor on silicon substrates with a Q factor corresponding to a range of 3 to 10 using multi-level spirals, or implemented the spiral inductor with high-resistance silicon substrates.
As another solution, bonding wires are used to rearrange the spiral inductor. However, this approach is limited to only certain circuit structures.
There also exists a method of implementing an inductor by a CMOS RFIC active element in which equivalent inductive impedance can be generated. Such an active inductor has major advantages of a high Q factor and reduced chip size, and includes latently tunable characteristics that the active inductor can be matched with on-chip filters and networks, and can be applied to LC tank circuits. However, the active inductor has the disadvantages of limited operation frequency range, high-noise characteristic, DC power consumption, and the like.
FIG. 1 is a diagram illustrating a grounded active inductor using a gyrator principle, as an example of a conventional active inductor.
An input impedance of the active inductor of FIG. 1 is defined as:
                                          Z                          i              ⁢                                                          ⁢              n                                ⁡                      (            s            )                          =                                            g                              ds                ⁢                                                                  ⁢                1                                      +                          s              ⁡                              (                                                      C                                          gs                      ⁢                                                                                          ⁢                      2                                                        +                                      C                                          gd                      ⁢                                                                                          ⁢                      1                                                        +                                      C                                          gd                      ⁢                                                                                          ⁢                      2                                                                      )                                                                        (                                                g                                      ds                    ⁢                                                                                  ⁢                    1                                                  +                                  g                                      m                    ⁢                                                                                  ⁢                    1                                                  +                                  sC                                      gd                    ⁢                                                                                  ⁢                    2                                                              )                        ⁢                          (                                                g                                      m                    ⁢                                                                                  ⁢                    2                                                  +                                  s                  ⁡                                      (                                                                  C                                                  gs                          ⁢                                                                                                          ⁢                          2                                                                    +                                              C                                                  gd                          ⁢                                                                                                          ⁢                          1                                                                                      )                                                              )                                                          (        1        )            where Cgd1 denotes a gate-drain capacitance for a transistor M1, Cgs2 and Cgd2 denote a gate-source capacitance and a gate-drain capacitance for a transistor M2, respectively, gm1 denotes a transconductance of a current source I1, gm2 denotes a transconductance of a current source I2, gds1 denotes an equivalent output conductance for the transistor M1, and ‘s’ equals jω.
Equation (1) shows an impedance characteristic having one zero and two poles. The zero exists in a place with a frequency of ωz≈gds1/(Cgs2+Cgd1+Cgd2), and the poles exist in a place with a frequency of ωp=gm2/Cgs2.
The active inductor of FIG. 1 has an advantage in that it provides a high gain and a high Q factor with a small size, but has a disadvantage of a very narrow operating frequency range between a zero frequency ωz and a gain bandwidth fT of the transistor M2.
FIG. 2 is a diagram illustrating a cascode-grounded active inductor further including a transistor M3 connected to the drain of the transistor M1 in the active inductor of FIG. 1, as another example of a conventional active inductor. The active inductor of FIG. 2 is an active inductor whose zero frequency ωz is reduced by minimizing the output conductance gds1 to widen the operating frequency rage in the active inductor of FIG. 1.
In the active inductor of FIG. 2, although its output impedance Zout increases from adding the transistor M3, the gds1 decreases, causing a decrease in the zero frequency ωz. As a result, the active inductor of FIG. 2 has a wide operating frequency range. Disadvantageously, however, the active inductor of FIG. 2 has a low gain and a low Q factor.
FIG. 3 is a diagram illustrating a cascode-grounded active inductor further including a feedback resistor Rf in the active inductor of FIG. 2, as another example of a conventional active inductor.
The feedback resistor Rf forms an additional inductive reactance of impedance at the source of the transistor M2. Such an inductive reactance can considerably increase an inductance. In addition, the increase in the inductance increases the Q factor.
Basically, however, the active inductor of FIG. 3 has a disadvantage in that it is impossible to tune an inductance value, a self-resonant frequency ω, and a peak Q frequency fQ. Furthermore, an increase in value of the feedback resistor Rf increases the inductance value but decreases the self-resonant frequency ω and the peak Q frequency fQ, making it difficult to use a high inductance value at a high frequency.